Computational predictability of time-dependent natural convection flows in enclosures (including a benchmark solution). (English) Zbl 1025.76042

Summary: This paper summarizes the results from a special session dedicated to understanding the fluid dynamics of the 8:1 thermally driven cavity which was held at the First MIT Conference on Computational Fluid and Solid Dynamics in June, 2001. The primary objectives for the special session were to: (1) determine the most accurate estimate of the critical Rayleigh number above which the flow is unsteady, (2) identify the correct, i.e. best time-dependent benchmark solution for the 8: 1 differentially heated cavity at particular values of the Rayleigh and Prandtl numbers, and (3) identify those methods that can reliably provide these results.


76M99 Basic methods in fluid mechanics
76R10 Free convection
80A20 Heat and mass transfer, heat flow (MSC2010)


Full Text: DOI


[1] Winters, Journal of Heat Transfer 109 pp 894– (1988)
[2] Onset of unsteadiness, routes to chaos and simulations of chaotic flows in cavities heated from the side: a review of present status. In Proceedings of the Tenth International Heat Transfer Conference, Brighton, UK (ed.). Rugby, Warwickshire, UK: Institution of Chemical Engineers 1994; 281-296.
[3] Gill, Journal of Fluid Mechanics 26 pp 515– (1966)
[4] Gadoin, International Journal for Numerical Methods in Fluids 37 pp 175– (2001)
[5] Personal communication, July 2000.
[6] Gresho, International Journal for Numerical Methods in Fluids 4 pp 557– (1984)
[7] (ed.). First MIT Meeting on Computational Solid and Fluid Mechanics, vols. 1 and 2. MIT Elsevier: New York, 2001.
[8] Finite difference methods for natural and mixed convection in enclosures. In Proceedings of the 8th International Heat Transfer Conference, ASME, August 1986; 101-109.
[9] Transition to unsteady natural convection of air in vertical differentially heated cavities influence of thermal boundary conditions on the horizontal walls. In Proceedings of International Heat Transfer Conference ASME, August 1986.
[10] Le Quéré, Journal of Fluid Mechanics 359 pp 81– (1998)
[11] Incompressible Flow and the Finite Element Method, vol. 2, Isothermal Laminar Flow. Wiley: Chichester, England, 2000.
[12] Finite element computer program for incompressible flow problems. Part 1?theoretical background. Technical report, Sandia National Laboratories, April 1987.
[13] Le Quéré, Journal of Heat Transfer 112 pp 965– (1990)
[14] De Vahl Davis, International Journal for Numerical Methods in Fluids 3 pp 227– (1983) · Zbl 0538.76075
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.